Publications

2004

• Topological derivative applied to cavity identification from elastodynamic data
  
  • Bonnet Marc
  • Guzina Bojan B
  , 2004, pp.355-362. This article is concerned with the use of topological derivative as a tool for preliminary elastic-wave probing of bounded or unbounded solids for buried objects. A formulation for computing the topological derivative field, based on an adjoint solution, is presented. A set of numerical results is included to illustrate the utility of topological derivative for outlining the cavity location and size prior to doing an actual inversion of measurements. The results presented here were obtained from a BIE solution, but the proposed methodology is applicable to other computational platforms such as the finite element method. (10.3166/reef.13.425-436)
  DOI : 10.3166/reef.13.425-436
• Stabilité de la forme de la goutte d'eau formée entre deux grains solides: méthode de résolution
  
  • Bérest Pierre
  • N'Dri Erik
  • Malinsky Laurent
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2004, 332, pp.665-672. On discute le signe de la seconde variation d'une Action lagrangienne en présence d'une contrainte intégrale, lorsque les conditions d'extrémité ne sont pas fixées, dans le cas où le lagrangien ne dépend pas explicitement de la variable d'intégration. Les résultats sont illustrés par le problème d'une goutte de liquide s'appuyant sur deux grains symétriques. (10.1016/j.crme.2004.01.015)
  DOI : 10.1016/j.crme.2004.01.015
• On Friction-Induced Instabilities and Vibrations
  
  • Nguyen Quoc Son
  Vietnam Journal of Mathematics, Springer, 2004, 32, pp.105-119. Some problems of friction-induced instabilities, vibrations and noise emissions are considered in this paper. The presentation is focussed on the possibility of flutter instability of the steady sliding equilibrium of an elastic solid in unilateral contact with a moving obstacle. The system of governing equations is given to obtain the steady sliding equilibrium and to discuss its stability. It is shown that the steady sliding equilibrium is generically unstable by flutter. This instability leads to a dynamic response which can be periodic or chaotic. Principal results of the literature are reported here. In the spirit of Hopf bifurcation, the existence problem of periodic solutions has been discussed in my research team for an academic problem of coaxial cylinders. It has been shown by a semi-analytical approach that an interesting family of these periodic solutions are stick-slip-separation waves propagating on the contact surface in a similar way as Schallamach waves in statics. The transition from a given position near equilibrium to the propagation of waves has been illustrated by a numerical approach using finite element simulations. Some phenomena of nonlinear vibration and noise emission in the daily life, such as brake squeal for example, can be discussed in this spirit.
• The origin of nucleation peak in transformational plasticity
  
  • Truskinovsky Lev
  • Vainchteyn Anna
  Journal of the Mechanics and Physics of Solids, Elsevier, 2004, 52, pp.1421-1446. A typical stress-strain relation for martensitic materials exhibits a mismatch between the nucleation and propagation thresholds leading to the formation of the nucleation peak. We develop an analytical model of this phenomenon and obtain specific relations between the macroscopic parameters of the peak and the microscopic characteristics of the material. Although the nucleation peak appears in the model as an interplay between discreteness and nonlocality, it does not disappear in the continuum limit. We verify the quantitative predictions of the model by comparison with experimental data for cubic to monoclinic phase transformation in NiTi. (10.1016/j.jmps.2003.09.034)
  DOI : 10.1016/j.jmps.2003.09.034
• Energetical approach in non-linear mechanics Lecture Notes 11
  
  • Stolz Claude
  , 2004, pp.108.
• Propagation of a shock discontinuity in an elasto-plastic material: constitutive relations
  
  • Dequiedt Jean-Lin
  • Stolz Claude
  Archives of Mechanics, 2004, 56,5, pp.391-410. The shock discontinuity problem is analyzed in the case of elastoplastic materials ; the jump relations for internal state variables cannot be exhibited directly. For this purpose, we solve the internal shock structure problem, assuming that the shock front is a continuous transition in a thin layer, taking account of dissipative effects. The shock generating function is introduced. The canonical equations of the shock structure are determined in the general case when the evolution of plasticity is derived from a pseudo potential of dissipation. The plane wave is analyzed for an isotropic material obeying a von Mises criterion, assuming that inside the shock the material is under pure axial compression: the existence and uniqueness results are established.
• Lamellar grains distribution and plastic strain heterogeneities in TiAl cast samples. Experiments and modelling
  
  • Gélébart Lionel
  • Bornert Michel
  • Bretheau Thierry
  • Caldemaison Daniel
  • Crépin Jérôme
  • Zaoui André
  Matériaux et Techniques, EDP Sciences [1970-....], 2004 (1-2), pp.69-75. During the cooling of TiAl cast alloys, the distribution of the dual-phase lamellar grains [ Ti$_3$Al ($\alpha_2$) $+$ TiAl ($\gamma$)] generates a so-called 'macrostructure'. Because of the highly anisotropic plastic behaviour of the lamellar grains, the distribution of the plastic strain is strongly influenced by such a macrostructure. This heterogeneity is clearly observed by means of a strainfield measurement technique applied to a compression test performed on a cast sample having a 'radial' macrostructure. As a result, a sample having such a macrostructure is not representative of the material and can not be used directly to evaluate 'material parameters'. Moreover the mechanical simulations of cast components should take into account such heterogeneities at the scale of the component. This strong influence is experimentally demonstrated and a way to take it into account in a mechanical simulation is proposed. (10.1051/mattech:2004008)
  DOI : 10.1051/mattech:2004008
• Identification en géotechnique par une méthode basée sur le théorème des travaux virtuels
  
  • Deng D.
  • Nguyen-Minh D.
  Revue française de Géotechnique, edp sciences, 2004, 108, pp.57-69. Une nouvelle méthode de rétro-analyse basée sur le théorème des travaux virtuels a été proposée, avec l’établissement d’un nouveau critère d’identification, la minimisation d’une fonction erreur basée sur le théorème des travaux virtuels. La méthode est simple et facile à programmer, tout en étant efficace et robuste. Elle permet d’identifier les paramètres mécaniques du matériau et les paramètres du chargement, et s’applique aux problèmes non linéaires élastoplastiques. L’application de la méthode au cas réel illustre sa faisabilité pratique en géotechnique. (10.1051/geotech/2004108057)
  DOI : 10.1051/geotech/2004108057
• Multiscale modelling of titanium aluminides
  
  • Roos Arjen
  • Chaboche Jean-Louis
  • Gélébart Lionel
  • Crépin Jérôme
  International Journal of Plasticity, Elsevier, 2004, 20, pp.811-830. In this work a three-scale model of the mechanical behaviour of titanium aluminides is presented. The first scale transition between the macroscopic length scale and the scale of an individual $α_2$, $γ$ or lamellar $α_2 + γ$ grain is made using elastically self-consistent transformation field analysis (TFA) with anisotropic elasticity. The constitutive equations of the $α_2$ and $γ$-phases are obtained through the framework of crystal plasticity. The effective behaviour of the lamellar $α_2–γ$ phase, however, necessitates a second scale transition. This transition, derived from a system of linear equations for a multilayer, is obtained and shown to be equivalent to the formalism of transformation field analysis. Some simple simulations are presented to show the viability of the method. (10.1016/j.ijplas.2003.08.005)
  DOI : 10.1016/j.ijplas.2003.08.005
• Critère de fatigue polycyclique pour des métaux anisotropes: application au monocristaux
  
  • Cano Florian
  • Constantinescu Andrei
  • Maitournam Habibou
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2004, 332 (2), pp.115-121. Les critères de fatigue polycycliques fondés sur un passage macro–méso, initiés par Dang Van, ont essentiellement été utilisés pour des matériaux polycristallins. Dans les critères existants l'isotropie aux échelles macroscopique et mésoscopique joue un rôle crucial. L'objectif de ce travail est de revoir l'approche macro–méso en fatigue en tenant compte de l'anisotropie du matériau et en s'appuyant sur des résultats obtenus par Bui. Les applications possibles sont les aciers inclusionnaires ou encore des structures monocristallines comme les aubes de turbine en titane. (10.1016/j.crme.2003.11.005)
  DOI : 10.1016/j.crme.2003.11.005
• On a new computational method for the simulation of periodic structures subjected to moving loads: application to vented brake disks
  
  • Nguyen-Tajan Mac Lan
  • Maitournam Habibou
  • Maestro Luis
  Revue Européenne des Éléments Finis, HERMÈS / LAVOISIER, 2004, 13 (5-7), pp.627-636. The purpose of the paper is to present a new numerical method suitable for the computation of periodic structures subjected to repeated moving loads. It directly derives from the stationary methods proposed for cylindrical and axisymmetrical structures. Its mains features are the use of a calculation reference related to the moving loads and the periodic property of the thermomechanical response. These methods are developped by PSA and the Ecole Polytechnique, in order to design vented brake discs. In this paper, a brief description of the algorithm is first given and examples of numerical simulations of a vented brake disc are treated. (10.3166/reef.13.627-636)
  DOI : 10.3166/reef.13.627-636
• Full 3D investigation of the local strain field in particulate metal matrix composites
  
  • Bornert Michel
  • Doumalin Pascal
  • Maire Éric
  • Moulinec Hervé
  , 2004, pp.445-446.
• Optimisation des portiques élastoplastiques : état limite des portiques élastoplastiques sous chargement répété mobile
  
  • Adjovi Edmond Codjo
  • Gnanvo Cyprien
  • Foudjet Amos
  • Halphen Bernard
  Journal des Sciences pour l'Ingénieur, 2004, 4, pp.50-59. La présente étude propose la généralisation de la notion de l'état d'auto contrainte de provenance statique des contours fermés au premier théorème d'adaptation "Bleich–Melan" pour l'analyse élastoplastique des portiques sous un système de charges répétés mobiles. La formulation adoptée dans ce travail conduit à la programmation linéaire et nécessite l'utilisation de la méthode SIMPLEX. La méthode développée permet de définir l'état de contrainte réel d'un portique donné sous un chargement donné. Les résultats de l'étude sont complétés par une application numérique.
• Microstructure Influence on Damage Initiation in Zirconium Alloys
  
  • Elbachiri Kamal
  • Crépin Jérôme
  • Bretheau Thierry
  • Rebeyrolle Véronique
  , 2004.
• Fast multipole method applied to elastostatic BEM-FEM coupling
  
  • Margonari Massimiliano
  • Bonnet Marc
  , 2004, 83 (10-11), pp.700-717. BEM–FEM coupling is desirable for three-dimensional problems involving specific features such as (i) large or unbounded media with linear constitutive properties, (ii) cracks, (iii) critical parts of complex geometry requiring accurate stress analyses. However, for cases with a BEM discretization involving a large number NBEM of degrees of freedom, setting up the BEM contribution to the coupled problem using conventional techniques is an expensive task. Moreover, the fully-populated BEM block entails a storage requirement and a contribution to the solution time via usual direct solvers. To overcome these pitfalls, the BEM contribution is formulated using the fast multipole method (FMM) and the coupled equations are solved by means of an iterative GMRES solver. Both the storage requirements and the solution times are found to be close to O(NBEM). A preconditioner based on the sparse approximate inverse of the BEM block is shown to improve the convergence of the GMRES solver. Numerical examples involving NBEM = O(105 − 106) unknowns, run on a PC computer, are presented; they include the Eshelby inclusion (as a validation example), a many-inclusion configuration, and a dam structure. (10.1016/j.compstruc.2004.09.007)
  DOI : 10.1016/j.compstruc.2004.09.007
• L'EBSD: un outil pour la micromécanique des materiaux
  
  • Caldemaison D.
  • Crépin Jérôme
  • Dexet M.
  • Gélébart L.
  , 2004, pp.87-100.
• Giens 2003
  
  • Bonnet Marc
  • Ben Dhia Hachmi
  • Allix Olivier
  , 2004.
• Initiation and propagation of fracture in the models of Griffith and Barenblatt
  
  • Marigo Jean-Jacques
  • Truskinovsky Lev
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2004, 16, pp.391-409. In the setting of the simplest debonding problem we give a systematic comparison of the fracture models due to Griffith and Barenblatt. We prove that the Griffith model represents an asymptotic Γ-limit of the Barenblatt model, when the ratio of the external and internal lengths increases indefinitely. We then illustrate the character of convergence by solving explicitly two sample problems with “initially rigid” and “initially elastic” cohesive energies. The geometrical simplicity of the setting allows us to study the small parameter dependence of both global and local minimizers of the total energy. (10.1007/s00161-003-0164-y)
  DOI : 10.1007/s00161-003-0164-y
• Simulating wear under cyclic loading by a minimization approach
  
  • Peigney Michaël
  International Journal of Solids and Structures, Elsevier, 2004, 41, pp.6783-6799. A new method is developed to determine the asymptotic state reached by a solid continuum subjected to wear and submitted to a cyclic loading. The main idea is to express the stabilized state as the solution of a minimization problem. This approach is applied to the wear problem of a half-plane in contact with a cyclically moving indenter. (10.1016/j.ijsolstr.2004.05.022)
  DOI : 10.1016/j.ijsolstr.2004.05.022
• Mechanics of low-angle extensional shear zones at the brittle-ductile transition
  
  • Gueydan F.
  • Leroy Y.
  • Jolivet Laurent
  Journal of Geophysical Research, American Geophysical Union, 2004, 109 (B12407), pp.1-16. Low-angle midcrustal ductile shear zones and the related microseismic activity recorded below regions of active extension are seen here as two consequences of strain localization. The feldspar-to-mica reaction which occurs once feldspar grains are fractured is the destabilizing mechanism selected to explain the strain localization. The model problem considered to substantiate these claims is solved by numerical means and combines the simple shear due to the rigid gliding of the upper crust (at the velocity of V s ) and the stretch resulting from the extension of the whole crust (at the velocity V e ). The rheological model accounts for dislocation creep of quartz, feldspar, and mica, the feldspar-to-mica reaction, and its prerequisite, which is the feldspar fracturing detected by the Mohr-Coulomb criterion. The one-dimensional (1-D) solution, which constrains shear bands to be horizontal, shows the depth partitioning in deformation mode between the simple shear of the low-viscosity deep crust and the stretching of the highly viscous midcrust. Strain localization occurs during rapid increase of the shearing velocity V s , corresponding to low values of the velocity ratio V e /V s . The 2-D solution (for V e /V s = 10−3) reveals the development of a periodic system of extensional shear bands, dipping at 30° toward the shearing direction at a depth of 12 to 14 km. Shear bands are formed after less than half a million years at the base of the reaction zone defined by the region where feldspar-to-mica reaction is completed. Shear bands do not propagate to greater depths because the pressure prevents the feldspar from fracturing and thus the reaction to occur. The periodic system of shear bands defines a midcrustal flat weakened zone within which the equivalent shear stress is enhanced by at least a factor of three at the shear band tips. Brittle fracture could thus occur within the midcrustal flat weakened zone, explaining therefore the microseismicity monitored at these depths in regions of active extension. (10.1029/2003JB002806)
  DOI : 10.1029/2003JB002806
• Propagation 3D de fissures dans l'inox 304L et simulations 2D d'évolutions de réseaux orthogonaux en fatigue biaxiale
  
  • Doquet V.
  • Kane A.
  , 2004. No abstract provided
• Nanocomposites base polymère renforcés par des particules rigides
  
  • Chabert Emmanuelle
  • Chazeau Laurent
  • Gauthier Catherine
  • Dendievel Rémy
  • Cavaillé Jean-Yves
  Mechanics & Industry, EDP Sciences, 2004, 5, pp.489-496. Les matériaux composites à base polymère montrent, dans certains cas, des comportements mécaniques spécifiques lorsque la taille des renforts particulaires rigides devient nanométrique. Il semble que cette particularité provienne du fait que les distances inter-particulaires moyennes sont alors comparables aux dimensions caractéristiques des chaînes polymères. On observe parfois des effets de renfort beaucoup plus importants que pour des composites classiques qui peuvent être attribués à l'existence de réseaux particule/macromolécule/particule ou encore de réseaux rigides de particules. Dans cette courte revue, l'effet du facteur de forme, de la fraction volumique et du procédé de mise en oeuvre sont discutés, ainsi que l'état de l'art en ce qui concerne la modélisation dans les domaines linéaire et non linéaire. (10.1051/meca:2004049)
  DOI : 10.1051/meca:2004049
• A computational approach to thermomechanical fatigue
  
  • Constantinescu Andrei
  • Charkaluk Eric
  • Lederer Guy
  • Verger Laetitia
  International Journal of Fatigue, Elsevier, 2004, 26, pp.805-818. This paper presents a computational approach for the lifetime assessment of structures under thermomechanical loading. One of the main features of the work is the search for simplicity and robustness in all steps of the modeling, in order to match the proposed method with industrial constraints. Among the peculiarities of the engineering environment are the imposed commercial computer programs and the short time delays for manufacturing. The proposed method is composed of a fluid flow, a thermal and a mechanical finite element computation, as well as a final fatigue analysis. The efficiency of the approach is proved by comparison with experimental results on prototype manifolds. The numerical results match both the localization of the damage zone and the lifetime. (10.1016/j.ijfatigue.2004.01.006)
  DOI : 10.1016/j.ijfatigue.2004.01.006
• Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap
  
  • Bui Huy Duong
  • Constantinescu Andrei
  • Maigre Hubert
  Inverse Problems, IOP Publishing, 2004, 20, pp.993-1001. This paper considers the identification problem of a linear crack in a body of finite extension within the framework of linear two-dimensional elastodynamics. In a series of prior papers in electricity, elasticity or acoustics, it has been proved using the reciprocity gap that three different series of adjoint wave fields determine in closed-form solution the normal of the plane of the crack, the position of the plane and finally the complete crack extension. The work developed next within the framework of linear elastodynamics defines a novel instantaneous reciprocity gap as the instantaneous work done by the adjoint tractions on the crack opening displacement. This quantity is then used to identify linear cracks in a two-dimensional problem. It is shown using a numerical example that a unique family of planar shear waves permits the identification of the normal, position and a convex hull of a linear crack through simple interpretations of the instantaneous reciprocity gap. This method is more general in the sense that it applies to three-dimensional problems as well. (10.1088/0266-5611/20/4/001)
  DOI : 10.1088/0266-5611/20/4/001
• Multiscale analysis of the transverse properties of Ti-based matrix composites reinforced by SiC fibres: from the grain scale to the macroscopic scale
  
  • Carrère Nicolas
  • Valle Roger
  • Bretheau Thierry
  • Chaboche Jean-Louis
  International Journal of Plasticity, Elsevier, 2004, 20, pp.783-810. It is well known that the presence of continuous fibres in SiC/Ti composites leads to a high mechanical anisotropy of the composite between the longitudinal and the two transverse directions. But it is also possible that the crystallographic texture of the matrix may lead to a non-negligible anisotropy of the mechanical properties of the composite. The crystallographic orientation of the matrix grains was determined using the Electron BackScattering Diffraction technique. A local texture of the matrix of the composite is thus evidenced. Finite Element calculations are used to determine the stress field in the matrix resulting from an applied transverse loading. The representative mechanical quantities thus determined are discussed in relation with the fundamental mechanisms of plastic deformation of the matrix. Finally, the crystallographic texture of the matrix of the composite is taken into account in the numerical modellings using a three-scale model that combines crystal plasticity, a polycrystalline aggregate model and a periodic homogenization through a Finite Element unit cell for the composite analysis. (10.1016/j.ijplas.2003.09.001)
  DOI : 10.1016/j.ijplas.2003.09.001